Impact of Regulations and Emissions
Exploratory data analysis
Quang-Vinh Do, Shaafici Ali, Thinh Hong, Youssef Makboul
2019-12-13
Introduction and Objectives
The event of climate change has been a frequently discussed topic especially as of late. Although a considerable amount of people deny the magnitude of the event, there is an increased fear of the general repercussions of global warming. This fear has lead to a significant public pressure being applied to governments around the world demanding increased regulations in order to help prevent climate change. This has been especially the case in late 2019 where protesters in increasing numbers demonstrated to spread awareness as well as encourage a greater response from legislators. In addition, the protesters also criticize the adherence to international protocols, thereby questioning the effect of global treaties on government greenhouse gas(GHG) emission legislation.
There are several possible reasons explaining the government reluctance. It may be the case that there is a negative economic impact in the imposing of strict emission regulation as emission could be related to economy growth. It could also be the case that governments have been imposing regulations as a result of international accords. In addition, it is possible that regulations are simply not effective enough to invoke a reduction in emissions.
In this report, we will attempt to gain insight on the reasons causing government reluctance as well as the global effect of protocol. This involves the following objectives :
- Identify relationship between total GHG emissions and total economic growth
- Identify relationship between environmental tax revenue and total GHG emissions
- Analyze the effect of international protocols on government emission legislation
- Identify relationship of total emission and particulate damage
Emission Relationships
Part of the objectives involve identifying and potentially quantifying a relationship between the total greenhouse gas emissions and different variables. These variables include the environmental tax revenue as well as the total economic growth. It is important to note that the goal is not to identify a cause or effect but rather discover a common relationship between the variables for a number of countries.
Definition of Variables
Total Growth
The total growth of an economy was measured by its annual growth rate. Moreover, the annual growth rate represents the percentage change in total growth of the country’s GDP. In this context, “total” refers to the sum among all sectors. The data set used for this was sourced from the Organisation for Economic Co-operation and Development(OECD) which provided the total growth per sub-sector(activity) for a given country per year.[1]
Total Emissions
The total emissions for a given country was measured by the sum of all of its greenhouse gas emissions for a given year. This includes the sum of the emissions of six gases classified as greenhouse gases. [2] The emission data was compiled over the course of over 20 years depending on the country.
Environmental Tax Revenue
The environmental tax revenue is expressed as the percentage of the given country’s GDP. These tax revenues are generated from a variety of environmental domains. These domains include energy products, vehicle fuels, motor vehicles and transport services as well as other various other industries that are subject to an environmental tax. [3]
Methodology
In order to gain insight on the relationship, a time series analysis is especially relevant. For each country, a separate time series for each of the respective variables was to be constructed. In every individual case, we wish to gain insight on whether one series’ changes is related to the other. We then evaluate the cross-correlations of the two time series using a cross correlation test with 95% confidence bounds.
To conduct a cross-correlation test, time series must be stationarized meaning that the mean and variance of the time series remains constant over time. To stationarized a given time series, differencing is necessary in which the change in value from one point is computed with a subsequent point in the time series. The stationarity of the time series is then confirmed by a ADF test as well as a KPSS test to test for trend-stationarity.
Raw Time Series
Differenced Time Series
This was accomplished by an automated procedure that would both stationarize ad-hoc and compute the cross-correlations for two given-time series.
##
## Autocorrelations of series 'X', by lag
##
## -10 -9 -8 -7 -6 -5 -4 -3 -2 -1
## 0.222 -0.446 0.282 -0.008 -0.070 0.058 -0.042 0.069 0.017 -0.489
## 0 1 2 3 4 5 6 7 8 9
## 0.813 -0.414 -0.156 0.351 -0.146 -0.082 0.031 0.085 0.082 -0.277
## 10
## 0.196This process was to be completed for each country in data set that had sufficient year entries in order to construct the time series. In this case the cutoff was seven years as this would allow us to test for a reasonable amount of countries due to data set limitations. The statistically significant(\(\alpha = 0.05\)) country cross-correlations are then plotted together onto an amalgamated ACF plot that can then be analyzed.
GHG Emissions and Economic Growth
Hypothesis
It was hypothesized that there would be a positive relationship between emissions and total economy growth. In other words, a rise in green-house gas emissions would be correlated with a rise in economic growth. This is mainly because it is believed that emissions are generally associated with an increased industrial output and thus, intuitively, a rise in emissions would be followed by an increase in economic growth.
This would ideally be demonstrated by the emission time series serving as a positive lagging indicator for the economic growth time series. This is where the effect of increase in the emission time series transfers to the economic growth time series several periods(years) later.
Results
The results were quite inconclusive but they did provide valuable insight. The resulting plot of cross-correlation was quite scattered with significant cross-correlations spread sparsely across the LAG axis. This can be observed in the plot below which represents the significant cross-correlations between economic growth and total emissions. This thus refuted our hypothesis as we expected cross-correlations to clearly tend to a negative lag with a positive cross-correlation.
Interestingly, there appeared to be clusters in the 0, -1 and 1 lags. Notably, the largest cluster was located at the 0 lag and had a strongly positive auto-correlation. This would indicate that a rise in emissions is directly auto-correlated with an increase in economic growth in the same year. However, this cluster size is not significant enough to draw that conclusion.
It was also difficult to draw a conclusion from the group of countries that were presented in this cluster. These countries included South Korea, Mexico, Netherlands, Slovakia, Turkey, United Kingdom, Slovenia, and the United States. It is possible that there is a shared economic attribute between these countries but it is not obvious.
Thus, the insight gained is that there is no evident cross-correlation between the total emission and economic growth for all countries. It could be the case that a significant cross correlation exists for countries with a specific economic attribute.
Flaws and Further Exploration
A major flaw in our methodology is that the significance level was not adjusted for the number of tests being done for each individual country. This is especially the case for evaluating the significance of the cross-correlations. This may have perhaps lead to more conclusive results.
A further analysis could have been to classify countries by development level and then evaluate their respective emission/growth cross-correlations. This could have added more insight in terms of meaning of the different cross-correlation clusters at different lags.
Environmental Tax Revenue and GHG Emissions
Hypothesis
For the purpose of our analysis, it is inferred that the an increase in environmental tax revenue can indicate either an increased violation of emission regulations by industries or stringent regulations that are difficult to observe. This is a reasonable assumption as the environmental tax revenue represents the government revenue generated from environmentally related taxes.
This leads us to believe that the environmental tax revenue will serve as a lagging indicator with the emission time series. In other words, total emissions will react to the change of environmental tax will transfer to the total emissions years later. It also believed that this relationship will be negatively cross-correlated meaning that an increase in environmental tax revenue will lead to decreased total emissions. This is ultimately evaluating the effectiveness of regulations in the reduction of emissions.
Results
The results provided valuable insight in determining the lagging relationship between the environmental tax revenue and the total emissions. However, the results were inconclusive in evaluating whether the relationship was positive or negative. The cross-correlation plot demonstrates all the significant cross-correlations between environmental tax revenue and emissions for 79 countries of various types of economies.
Upon inspection of the plot, the nature of the relationship is not easily determined as the cross-correlations do not have a clear positive or negative tendency. However, it can be inferred that the cross-correlations tend to have a negative lag as demonstrated by the lag density plot. Thus, it can be deduced that the environmental-tax revenue can serve as a lagging indicator for the total emissions of a given country. This can potentially indicate that emissions react to a change in environmental taxes.
Flaws and Further Exploration
Again, major flaw in our methodology is that the significance level was not adjusted for the number of tests being done for each individual country. Another potential flaw is that multiple variables affecting the environmental tax revenue were not considered. For instance, it could be the case that the environmental tax revenue was under reported in developing countries as there is likely to be bribes in place in exchange for tax breaks.
To remedy this potential inaccuracy, it would have been better to classify countries based on a corruption index to then analyse the emission reaction to environmental tax revenues.
Also, a further analysis could have been to classify countries by economy type as this can heavily affect the environmental tax revenues as well as the emissions. For instance, an heavily industrial economy will have different emission reactions as a relatively green economy since it may be more difficult to adjust emission levels since the emission are integral to the country’s output.
Kyoto Protocol
Do regulations have any effect in reducing the amount of GHG emissions?
Who are the biggest producers of GHG
We can start with a high level view and plot the ghg emissions per country to determine if certain areas have much higher amounts of emissions compared to others and to get a basic sense of which countries pollute the most.
China and US have are by far the greatest GHG emitters. Next, we see Brazil, Russia, India, Japan, and others with noticeable amounts of GHG emissions. The other countries seem to have much lower amounts of emissions, however it looks like overall the more developed countries are emitting more.
We will limit our analysis to the countries with the highest total GHG emissions. We decided that it would be more insightful to analyze this subset of countries as they have the most impact on climate change. For our subset, we chose the top countries making up 80% of the global GHG emissions.
As shown in the above plot, there are 29 countries making up the top 80% of global emissions. US and China account for nearly 1/3 of global emissions at 31% while the other countries are more balanced in emissions.
Did the Kyoto Protocol have an effect on GHG emissions?
Now that we have a subset of important countries to analyze, we want to determine if regulations have any impact on reducing GHG emissions. In particular, we will focus on the Kyoto Protocol which was an international treaty where parties are committed to reduce green house gas emissions. The Kyoto Protocol was effective as of February 16, 2005 and is currently ongoing for its second commitment period. We have manually checked on the United Nations Climate Change website that all 29 countries of interest were part of the protocol as of 2005 (as the data was not available for use).
Note that Canada withdrew in December 2012 however for this analysis we will examine the impact of the protocol being implemented as of 2005 and onward. As well, since the emission data is yearly we will assume that the emissions for year 2005 were under the Kyoto Protocol.
Global effect
First let’s see how the Kyoto Protocol effected the global GHG emissions.
Just from eyeballing the plot it doesn’t look like the Kyoto Protocol had any impact on global GHG emissions as it seems to be climbing at the same rate as it was before the protocol. To confirm this, we will attempt to apply intervention analysis by modelling the time series as a regression with arima errors and determine if the coefficient is significant. The model is expressed as:
\(y_t = \beta_0 + \beta_1 x_t + \eta_t\) where \(\eta'_t = \phi_1 \eta'_{t-1} + \varepsilon_t\)
\(x_t\) is a vector of 0,1 where it’s 0 if is before the Kyoto Protocol effective date and 1 if after.
Note, this simply checks for constant changes to the mean value.
With this definition we get the following regression with arima errors model 
## Series: .
## Regression with ARIMA(2,0,0) errors
##
## Coefficients:
## ar1 ar2 intercept xreg
## 1.6464 -0.6582 39893.183 268.3900
## s.e. 0.1450 0.1486 5470.291 493.7005
##
## sigma^2 estimated as 400068: log likelihood=-197.23
## AIC=404.46 AICc=407.62 BIC=410.55
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 165.3836 579.7044 431.8415 0.3898579 1.116764 0.6609637
## ACF1
## Training set -0.2412943The best model found using the AIC is a regression with errors ARIMA(2,0,0) meaning it’s auto regressive only. It has fairly good performance metrics on the training set. Now we analyze residuals.
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(2,0,0) errors
## Q* = 5.4648, df = 3, p-value = 0.1408
##
## Model df: 4. Total lags used: 7
From the Ljung-Box test we get a p-value of 0.1408 which is fairly high so we can conclude that there’s no autocorrelation between the errors. As well, the residuals seem to follow a normal distribution from the qq-plot shown and also seems like random noise which indicates that the model has captured the proper patterns. Thus, the regression model with arima errors does a good job of modelling the time series.
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 1.64637 0.14503 11.3519 < 2.2e-16 ***
## ar2 -0.65822 0.14861 -4.4292 9.458e-06 ***
## intercept 39893.18297 5470.29099 7.2927 3.038e-13 ***
## xreg 268.38997 493.70053 0.5436 0.5867
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1From the output above of the p-values for the parameters it shows that xreg is not significant at all with a very high p-value of 0.5867. Thus we can conclude since the xreg parameter was not significant, then it does not add much information for the model and that the period after the Kyoto Protocol start date was not much different from before. Therefore the Kyoto Protocol didn’t have much impact on global GHG emissions!
Per country effect
We suspect that this might not be true for certain countries. Some countries might have actually shown a significant change in their ghg emissions after the Kyoto Protocol. We will apply the same process as we did for World emissions but for our 29 countries of interest. Let’s start by viewing the ghg emissions over time for all countries.
By eyeballing the plot, it does not seem like any single country’s GHG emissions changed much after the Kyoto Protocol in 2005. We can determine the significance by modelling all the countries each with a regression with arima errors. As we are doing multiple hypothesis tests, we will have to be more careful and apply the Bonferroni correction using an an alpha of \(0.05 / n\) where \(n\) is the number of tests. Note, there is some controversy about this correction however it is simple for now.
## [1] "Indonesia P-value: 6.0235477544006e-09"From the output Indonesia is the only country that had a significant p-value, in this case of 6.02e-09 which is extremely significant. Let’s view its emissions overtime to see what was found.
Since 2005, Indonesia has had a major increase in its GHG emissions and so the Kyoto Protocol doesn’t seem to have had an effect in reducing Indonesia’s GHG emissions. And neither did it have an effect for any of the other 28 countries either as they had non-significant p-values. Therefore, we can conclude that even at the per country level the Kyoto Protocol doesn’t seem to have had an impact in reducing GHG emissions. This confirms what we initially saw from the plot above as well.
Kyoto Protocol effects on regulations
So even after the Kyoto Protocol was implemented there was no significant change in GHG emissions, but how active were countries in creating regulations relating to climate change after the Kyoto protocol was put into place?
We can attempt to answer this question by simply viewing the number of regulations total that were put into place in between 2005-2019 and 1991-2005. We can compare the number of regulations created between Kyoto Protocol start until present date with between 1991 to Kyoto Protocol start. This gives 14 years on either sides pre/post protocol to compare with. For this analysis, we will include all countries.
Looks like there have been many more regulations that have been created after 2005 than before 2005 for the same time ranges. Just to confirm we will do a paired t-test of difference of means
##
## Paired t-test
##
## data: regulations_compare$pre_kyoto and regulations_compare$post_kyoto
## t = -17.336, df = 197, p-value < 2.2e-16
## alternative hypothesis: true difference in means is less than 0
## 95 percent confidence interval:
## -Inf -5.738715
## sample estimates:
## mean of the differences
## -6.343434As expected from just viewing the data, the p-value is extremely low of 2.2e-16 so we reject the null and we can say the means are significantly different from each other. This allows us to conclude that yes from 2005-2019 there have been more regulations than in 1991-2005 created by countries indicating that they are more active in climate change prevention, however we cannot necessarily conclude that it was due to the Kyoto Protocol. Note, we did not take into account the types or impacts of each individual regulation.
Conclusion
Overall, no the Kyoto Protocol did not have any significant impact on the reduction of GHG emissions however countries have been more active in creating regulations concerning climate change since the Kyoto Protocol was initiated, whether it was due to the Kyoto Protocol or not. So even though countries have been more active, it doesn’t show in the GHG emissions. This could be due to either regulations aren’t strict enough or perhaps targeted parties, or industries aren’t following the regulations, or even that the regulations aren’t targeting the biggest causes of GHG emissions. However, regardless of the reason we can definitely conclude that there needs to be more effort in order to reduce GHG emissions and that prior efforts have had little effect.
Assumptions/Comments
A better method for Intervention Analysis could’ve been applied to compare the time series before and after the Kyoto Protocol adoption
The exact GHG emissions used was total_ghg_emissions_including_land_use_change_and_forestry_mt_co_e as this included all emissions contributing to climate change
Better method for handling multiple hypothesis testing could’ve been applied. In this case, even if we did not account for it none of the results would’ve changed
For regulations per country, each regulation was counted equally and we did not take into account how one regulation has a larger impact than others in terms of what the regulation actually does
80% top country ghg emissions chosen was a bit arbitrary
Not all countries were admitted to the Kyoto Protocol at the same time at 2005. Since the data was not available for use we made the assumption that they all joined at 2005.
Suggestions for further work
Acquire monthly data to give more data points
View GHG emissions per capita instead. Population rises exponentially and has grown by a lot 6.5B in 2005 to 7.5B in 2019 so 1B change so of course we would expect that to cause greater emissions. We wouldn’t be surprised to see that the emissions per capita actually were affected after the Kyoto Protocol in 2005.
It would also be interesting to see the effects of regulations on a country and subsector view as we would expect certain industries to behave much more differently than others. The following plot shows for Canada the total GHG emissions per subsector and the points on the lines represent that a regulation was created on that year for that subsector. The second plot shows for Canada the energy subsector specifically along with actual names of regulations.
Particulate and Emissions Relationship
Definition
Long Definition: “Particulate emissions damage is the damage due to exposure of a country’s population to ambient concentrations of particulates measuring less than 2.5 microns in diameter (PM2.5), ambient ozone pollution, and indoor concentrations of PM2.5 in households cooking with solid fuels. Damages are calculated as foregone labor income due to premature death. Estimates of health impacts from the Global Burden of Disease Study 2016. Data for other years have been extrapolated from trends in mortality rates.” –World bank researcher
Statistical concepts used in collecting the data
" Within the national accounting framework, air pollution damages are estimated following a human capital approach. Damages from premature mortality are calculated as the present value of lost income during working age, 15-64. Premature mortality among children is valued by adjusting for years until working age and discounting more heavily into the future. Estimates are for both urban and rural areas. Exposure to household air pollution is proxied by the number of households in each country cooking with solid fuels." –world bank researcher
Why its relevant to developement
“Air pollution places a major burden on world health. In many places, including cities but also nearby rural areas, exposure to air pollution exposure is the main environmental threat to health. Long-term exposure to high levels of fine particulates in the air contributes to a range of health effects, including respiratory diseases, lung cancer, and heart disease, resulting in 3.2 million deaths annually according to the Global Burden of Disease 2010 study. Not only does exposure to air pollution affect the health of the world’s people, it also carries huge economic costs and represents a drag on development, particularly for low and middle income countries and vulnerable segments of the population such as children and the elderly.” - World Bank researcher
Reasoning
As the researcher stated in limitations, this provides an low end estimate of air pollution damage and exploring the relationship between emissions and particulate damage can help give a view between emissions and some of the damage it causes.
Emissions were measured as total CO2
There was a choice to choose between the particulate damage cost in terms of US$ or from the percentage of GNI%. GNI stands for Gross National Income and it is a measure of all the money earned as income from businesses and people. GNI gave a better measure of the relative burden then US dollars would have. If a coal miner and a billionaire both lost $50,000, the absolute value would be the same but the impact would be completely different.This logic was used in making this decision, not all countries have similar wealth so the impact must be measured.
In general the impact has been going down. An arima forecast of 25 years shows the trajectory of particulate damage for the average particulate damage per country. 
##View of the world.
A cross correlation was built for every country/territory in the world that is recognized by the world bank. The countries were put into 5 categories
1.No correlation
2.Positive correlation with increasing emissions
3.Positive correlation with decreasing emissions
4.Negative correlation with increasing emissions
5.Negative correlations with decreasing emissions
##Results 
##Issue with methodology
All these countries are not independent of each other. By doing a cross correlation over 200 times we run into multiple comparisons problem. The multiple comparisons problem is when multiple hypotheses are tested,the likelihood of a wrong inference/outlier result increases. We need to correct for that and in order to do so we need to first understand how significance of cross correlations are calculated.
##Correction and testing results
The significance levels for a cross correlation with a 0.05 threshold is calculated by \(\frac{2}{\sqrt{observations}}\) Observations in this case are all the years that have both particulate damage and emissions. A country was said to be positively correlated if there existed a lag year that had a significant relationship. There were some countries that had a positive correlation with some lags and also had a negative correlation with others. In general this was the break down of how the countries were categorized.
1.positive correlation between particulate damage and emissions 2.negative correlation between particulate damage and emissions 3.both positive and negative correlation depending on the lag year chosen 4.no correlation
## # A tibble: 1 x 4
## both positive negative none
## <int> <int> <int> <int>
## 1 7 28 113 17In general cross correlations significance level follows a normal distribution along 0 with a standard deviation of \(\frac{2}{\sqrt{observations} * 2}\) this was derived from the formula earlier for the 95% confidence interval, which is two standard deviations, so halving it will give us a good SD to use for simulations.
After running the experiment 1000 times These were the results for each category.
The actual results for each category is that black line shown. Using Dunn-Sidak correction the actual values must be either smaller than or equal to the bottom 3.108201410^{-4} percent of simulations or greater than or equal to 0.9996892 percent. The categories “both” and “positive” cross correlations are well within those ranges and we cannot determine if these results are not just due to chance and are not random.
But the number of negative cross correlations are significantly higher than all other simulated values and the number of no cross correlations are significantly lower. Therefor we can say that a relationship is there and that it should be explored more.
##Comments
One failing of the simulations is that even though it simulates cross correlation significance levels well, it doesn’t map the relationship between lag years well. If a significant relationship happens at year 0, it is very likely for there to also be a relationship at year 1 but the simulations did not take that into account.
Another issue is the fact that GNI for almost every country is continuously growing. So even if the damage is growing, the relative burden will likely always fall. A choice was made to go with GNI as opposed to US dollars for time but exploring that relationship could be worthwhile.
Suggestions for further explorations
particulate damage only provides a low estimate to the damage of air pollution. Exploring other metrics and adding them could be worthwhile and provide better insight.
References
Total Growth Per Country: https://data.oecd.org/natincome/value-added-by-activity.htm#indicator-chart
Total Emission Per Country: https://www.wri.org/resources/data-sets/cait-country-greenhouse-gas-emissions-data
Environmental Tax Revenue: https://data.oecd.org/envpolicy/environmental-tax.htm
Arima Modeling: https://otexts.com/fpp2/regarima.html
Datasets used
### Country Emission Data - Project path : “data/raw/CAIT-Country-CO2-Emissions-Energy-Sub-Sector.csv” - Other path: ‘data/raw/CAIT Country GHG Emissions/CAIT Country GHG Emissions.csv’ - URL : https://www.wri.org/resources/data-sets/cait-country-greenhouse-gas-emissions-data
### Value added(value generated by producing goods and services) per activity(sector) globally - Project Path : “data/raw/value_added_per_act.csv” - URL : https://data.oecd.org/natincome/value-added-by-activity.htm#indicator-chart
### Regulations per country - Project Path : “data/raw/law_search/data.csv” - URL : http://www.lse.ac.uk/GranthamInstitute/climate-change-laws-of-the-world/
### Environmental tax Revenue per country per year - Project Path : “data/raw/emission_tax.csv” - URL : https://data.oecd.org/envpolicy/environmental-tax.htm
### Employment by activity - Project Path : “data/raw/employment_per_act.csv” - URL : https://data.oecd.org/emp/employment-by-activity.htm ### Canada GHG Emissions - Project Path: “data/raw_emission_per_sect/GHG-emissions-sector-en.csv” - URL: https://www.canada.ca/en/environment-climate-change/services/environmental-indicators/greenhouse-gas-emissions.html
### Per Sector Emission - Source: “United Nations FAO” - URL : https://ourworldindata.org/co2-and-other-greenhouse-gas-emissions#emissions-by-sector #### CO2 per sector - Project Path : “data/raw/emission_per_sect/global-carbon-dioxide-emissions-by-sector.csv” #### Methane per sector - Project Path : “data/raw/emission_per_sect/methane-emissions-by-sector-gg-coe.csv” #### Nitrous Oxide per sector - Project Path : “data/raw/emission_per_sect/nitrous-oxide-emissions-by-sector.csv” #### Greenhouse gas emission per sector - Project Path : “data/raw/emission_per_sect/greenhouse-gas-emissions-by-sector.csv”